The gravitational potential of two homogeneous spherical shells `A` and `B` of same surface density at their respective centres are in the ratio `3:4`. If the two shells collapse into a single one such that surface charge density remains the same, then the ratio of potential at an internal point of the new shell to shell `A` is equal to

Options

A. `3:2`
B. `4:3`
C. `5:3`
D. `5:6`

Answer

C

Explanation

`4pi^(2)rho=4pir_(1)^(2)rhorArr r^(2)=r_(1)^(2)+r_(2)^(2)`
`V=(-GM)/r=-(G4pir^(3)rho)/r`
`V=-4pirGrhorArr Vpropr`
`(V_(1))/(V_(2))=(r_(1))/(r_(2))=3/4rArr (r_(1)^(2))/(r_(2)^(2))=9/16`
`r_(1)^(2):r_(2)^(2):r^(2)=r_(1)^(2):r_(2)^(2):(r_(1)^(2)+r_(2)^(2))=9:16:(9+16)`
`rArr r_(1):r_(2):r=3:4:5=V_(1):V_(2):V`